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3 years ago

which of the following numbers which of the following numbers when added to it perfect squares is 240

Mathematics

2 answers:

Sophie [7]3 years ago

5 0

15.5 will add up to 240 perfect square

Katena32 [7]3 years ago

4 0

Answer:

first of all square mean two number or double so if we multiple 15×15=225 and if we multiply 16×16=256 mean the number 240 lies between them what about number 15.5 lets try now 15.5×15.5=240.25 if you want to make sure so just take a square root of this number

$\sqrt{240.25} = 15.5$

so 240 is product of (15.5)² note number after point is negligible

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3. A rocket is launched from a height of 3 meters with an initial velocity of 15 meters per second.

Vikki [24]

Let the rocket is launched at an angle of \theta with respect to the positive direction of the x-axis with an initial velocity u=15m/s.

Let the initial position of the rocked is at the origin of the cartesian coordinate system where the illustrative path of the rochet has been shown in the figure.

As per assumed sine convention, the physical quantities like displacement, velocity, acceleration, have been taken positively in the positive direction of the x and y-axis.

Let the point P(x,y) be the position of the rocket at any time instant t as shown.

Gravitational force is acting downward, so it will not change the horizontal component of the initial velocity, i.e. $U_x=U cos\theta$ is constant.

So, after time, t, the horizontal component of the position of the rocket is

$x= U \cos\theta t \;\cdots(i)$

The vertical component of the velocity will vary as per the equation of laws of motion,

$s=ut+\frac12at^2\;\cdots(ii)$ , where,s, u and a are the displacement, initial velocity, and acceleration of the object in the same direction.

(a) At instant position P(x,y):

The vertical component of the initial velocity is, $U_y=U sin\theta$ .

Vertical displacement =y

So, s=y

Acceleration due to gravity is $g=9.81 m/s^2$ in the downward direction.

So, $a=-g=-9.81 m/s^2$ (as per sigh convention)

Now, from equation (ii),

$y=U sin\theta t +\frac 12 (-9.81)t^2$

$\Rightarrow y=U \sin\theta \times \frac {x}{U \cos\theta} +\frac 12 (-g)\times \left(\frac {x}{U \cos\theta} \right)^2$

$\Rightarrow y=U^2 \tan\theta-\frac 1 2g U^2 \sec^2 \theta\;\cdots(iii)$

This is the required, quadratic equation, where $U=15 m/s$ and $g=9.81 m/s^2$ .

(b) At the highest point the vertical velocity,v, of the rocket becomes zero.

From the law of motion, $v=u+at$

$\Rightarroe 0=U\sin\theta-gt$

$\Rightarroe t=\frac{U\sin\theta}{g}\cdots(iv)$

The rocket will reach the maximum height at $t= 1.53 \sin\theta s$

So, from equations (ii) and (iv), the maximum height, $y_m$ is

$y_m=U\sin\theta\times \frac{U\sin\theta}{g}-\frac 12 g \left(\frac{U\sin\theta}{g}\right)^2$

$\Rightarrow y_m=23 \sin\theta -11.5 \sin^2\theta$

In the case of vertical launch, $\theta=90^{\circ}$ , and

$\Rightarrow y_m=11.5 m$ and $t=1.53 s$ .

Height from the ground= 11.5+3=14.5 m.

(c) Height of rocket after t=4 s:

$y=15 \sin\theta \times 4- \frac 12 (9.81)\times 4^2$

$\Rightarrow y=15 \sin\theta-78.48$

$\Rightarrow -63.48 m >y> 78.48$

This is the mathematical position of the graph shown which is below ground but there is the ground at $y=-3m$ , so the rocket will be at the ground at t=4 s.

(d) The position of the ground is, y=-3m.

$-3=U\sin\theta t-\frac 1 2 g t^2$

$\Rightarrow 4.9 t^2-15 \sin\theta t-3=0$

Solving this for a vertical launch.

$t=3.25 s$ and $t=-0.19 s$ (neglecting the negative time)

So, the time to reach the ground is 3.25 s.

(e) Height from the ground is 13m, so, y=13-3=10 m

$10=U\sin\theta t-\frac 1 2 g t^2$

Assume vertical launch,

$4.9 t^2-15 \sin\theta t+10=0$ [using equation (ii)]

$\Rightarrow t=2.08 s$ and $t=0.98 s$

There are two times, one is when the rocket going upward and the other is when coming downward.

4 0

3 years ago

HELP!!<br> Which combination of limit properties is required to evaluate this limit?

damaskus [11]

Answer:

B. Sum difference, product, power

Step-by-step explanation:

To evaluate this limit we need to know how to get the limits involving sums and differences. Since powers are involved we need the power rule too. We use the product rule instead of the quotient rule because the fraction can be written as a product with a negative power.

7 0

4 years ago

Read 2 more answers

Maya is comparing ride-sharing company prices. Company M charges $1.75 per mile driven and a one-time trip fee of $5. Company N

BabaBlast [244]

Answer:

1.75x+5<2.5x+3

Step-by-step explanation:

4 0

3 years ago

HELPPP PLSSSSSSSSS!!!!!!!!!!

Diano4ka-milaya [45]

Answer:

box A surface area= 336 inch ^2

calculated using formula 2h(l+b)

box B surface area = 352 inch^2

calculated using same method.

hope this would help you!

5 0

3 years ago

Answer please due today

mezya [45]

Answer:

CD=9

Step-by-step explanation:

ΔABD=>

AD²=AB² + BD² [Pythagorean Theorem]

BD²= AD²-AB²

BD²=9²-3²

BD²=72

BD=√72=6√2....(1)

ΔBCD=>

CD²=BD²+BC²

CD²=(6√2)² + 3²

CD²=72+9

CD²=81

CD=√81

CD=9

5 0

3 years ago

which of the following numbers which of the following numbers when added to it perfect squares is 240 ​

which of the following numbers which of the following numbers when added to it perfect squares is 240